相关论文: Polynomial Time Symmetry and Isomorphism Testing f…

The graph isomorphism problem asks whether two graphs are identical up to vertex relabeling. While the exact problem admits quasi-polynomial-time classical algorithms, many applications in molecular comparison, noisy network analysis, and…

Given two tuples of subspaces, can you tell whether the tuples are isomorphic? We develop theory and algorithms to address this fundamental question. We focus on isomorphisms in which the ambient vector space is acted on by either a unitary…

The presented material is devoted to the equivalent conversion from the vertex graphs to the edge graphs. We suggest that the proved theorems solve the problem of the isomorphism of graphs, the problem of the graph's enumeration with the…

We prove that the combinatorial Weisfeiler-Leman algorithm of dimension $(3k+4)$ is a complete isomorphism test for the class of all graphs of rank width at most $k$. Rank width is a graph invariant that, similarly to tree width, measures…

We solve the subgraph isomorphism problem in planar graphs in linear time, for any pattern of constant size. Our results are based on a technique of partitioning the planar graph into pieces of small tree-width, and applying dynamic…

We present a simple iterative strategy for measuring the connection strength between a pair of vertices in a graph. The method is attractive in that it has a linear complexity and can be easily parallelized. Based on an analysis of the…

Given a function $f$ in a finite field ${\mathbb F}_q$ of $q$ elements, we define the functional graph of $f$ as a directed graph on $q$ nodes labelled by the elements of ${\mathbb F}_q$ where there is an edge from $u$ to $v$ if and only if…

We show that a simple Markov chain, the Glauber dynamics, can efficiently sample independent sets almost uniformly at random in polynomial time for graphs in a certain class. The class is determined by boundedness of a new graph parameter…

We investigate the computational complexity of finding temporally disjoint paths or walks in temporal graphs. There, the edge set changes over discrete time steps and a temporal path (resp. walk) uses edges that appear at monotonically…

We propose an algorithm for solving of the graph isomorphism problem. Also, we introduce the new class of graphs for which the graph isomorphism problem can be solved polynomially using the algorithm.

Properties of the `$k$-equivalent' graph families constructed in Cai, F\"{u}rer and Immerman, and Evdokimov and Ponomarenko are analysed relative the the recursive $k$-dim WL method. An extension to the recursive $k$-dim WL method is…

Joint time-vertex graph signals are pervasive in real-world. This paper focuses on the fundamental problem of sampling and reconstruction of joint time-vertex graph signals. We prove the existence and the necessary condition of a critical…

In network theory, a question of prime importance is how to assess network vulnerability in a fast and reliable manner. With this issue in mind, we investigate the response to parameter changes of coupled dynamical systems on complex…

In this paper we introduce a novel polynomial-time algorithm to compute graph invariants based on the modified random walk idea on graphs. However not proved to be a full graph invariant by now, our method gives the right answer for the…

Diverse facets Of the Theory of Quantum Walks on Graph are reviewed Till now .In specific, Quantum network routing, Quantum Walk Search Algorithm, Element distinctness associated to the eigenvalues of Graphs and the use of these relation…

A hole in a graph G is an induced cycle of length at least four; an antihole is a hole in the complement of G. In 2005, Chudnovsky, Cornuejols, Liu, Seymour and Vuskovic showed that it is possible to test in polynomial time whether a graph…

We introduce the framework of Deep Weisfeiler Leman algorithms (DeepWL), which allows the design of purely combinatorial graph isomorphism tests that are more powerful than the well-known Weisfeiler-Leman algorithm. We prove that, as an…

Uniform sampling from graphical realizations of a given degree sequence is a fundamental component in simulation-based measurements of network observables, with applications ranging from epidemics, through social networks to Internet…

Graph-based tests are a class of non-parametric two-sample tests useful for analyzing high-dimensional data. The test statistics are constructed from similarity graphs (such as K-minimum spanning tree), and consequently, their performance…

We study finite graphs embedded in oriented surfaces by associating a polynomial to it. The tools used in developing a theory of such graph polynomials are algebraic topological while the polynomial itself is inspired from ideas arising in…